Yixin He

collaborators

6 papers

math.CV2026

Optimal universal growth for integral means of normalized logarithmic derivatives in the Carathéodory class

Yixin He, Quanyu Tang, Teng Zhang

We determine the optimal universal growth scale for the integral means of normalized logarithmic derivatives in the Carathéodory class. This resolves a problem of D.~K.~Thomas.

math.CV2026

A Solution to a Problem of Rubel on Two-Parameter Normal Families of Entire Functions

Yixin He, Quanyu Tang, Teng Zhang

We construct an entire function $F (z, a, b) \in O (C^{3})$ such that the family ${F (\cdot, a, b) : a, b \in C}$ of entire functions of $z$ is normal on…

math.CO2026

An Erdős--Trotter problem on antichains with multiplicity $r$ on each occurring level

Yixin He, Quanyu Tang

Fix an integer $r \geq 2$ . For each $n$ we consider families $F \subseteq 2^{[n]}$ that form an antichain and have the property that, for every $t$ , if there exists $A\in\math…

math.CV2026

On Fuchs's additive intersection problem for the hyperbolic metric

Yixin He, Quanyu Tang

For hyperbolic domains $D_{1}, D_{2} \subset {z \in C : ∣ z ∣ < R}$ and $z \in D_{1} \cap D_{2}$ , we consider the ratio $\frac{λ _{D_{1} \cap D_{2}} ( z )}{λ _{D_{1}} ( z ) + λ _{D_{2}} ( z )} .$ We solve a pr…

math.CV2026

Generalizing the Clunie--Hayman construction in an Erdős maximum-term problem

Yixin He, Quanyu Tang

Let $f (z) = \sum_{n \geq 0} a_{n} z^{n}$ be a transcendental entire function and write $M (r, f) := max_{∣ z ∣ = r} ∣ f (z) ∣$ and $μ (r, f) := max_{n \geq 0} ∣ a_{n} ∣ r^{n}$ . A problem of Erdős asks for the valu…

math.GM2024

A Note on a Recent Attempt to Prove the Irrationality of $ζ (5)$

Keyu Chen, Wei He, Yixin He +7

Recently Shekhar Suman [arXiv: 2407.07121v6 [math.GM] 3 Aug 2024] made an attempt to prove the irrationality of $ζ (5)$ . But unfortunately the proof is not correct. In this note, we…

Optimal universal growth for integral means of normalized logarithmic derivatives in the Carathéodory class

A Solution to a Problem of Rubel on Two-Parameter Normal Families of Entire Functions

An Erdős--Trotter problem on antichains with multiplicity r on each occurring level

On Fuchs's additive intersection problem for the hyperbolic metric

Generalizing the Clunie--Hayman construction in an Erdős maximum-term problem

A Note on a Recent Attempt to Prove the Irrationality of ζ(5)

An Erdős--Trotter problem on antichains with multiplicity $r$ on each occurring level

A Note on a Recent Attempt to Prove the Irrationality of $ζ (5)$